For a given value of the integration time, source repetition rate, \(\eta _{\mathrm {loss}}\) , \(QBER_I\)  and \(p_{ec}\) , we will calculate the secure key length. Initially, this involves optimizing the secure key length by varying the parameters: \(\lbrace P^A_X, p_{\mu _1},p_{\mu _2},\mu _1,\mu _2\rbrace \) . The value of \(P^B_X\)  will either be set equal to \(P^A_X\)  or will be fixed. The smallest intensity, \(\mu _3\)  should be set to zero, but to avoid numerical issues, we instead use a very small value, \(\mu _3=10^{-9}\) . The details of the optimization are the same as those presented in [1]} with the exception that now the channel loss is assumed to be fixed in time.
